Superstable single-step methods for second-order initial-value problems

摘要

Single-step methods of orders four and six are derived for the numerical integration of general second-order initial-value problems y″ = f(x, y, y′), y(x0) = y0, y′(x0) = y′0. The methods when applied to the test equation y″ + 2αy′ + β2y = 0, α, β ⩾ 0, α + β > 0 are superstable in the sense of Chawla [1] with the exception of a finite number of isolated values of βh. Numerical results demonstrate the efficiency of the methods.